The measure of a single angle in a regular octagon is (4x + 12)°. Find the value of x. Show equations and all work that leads to your answer.
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To find the value of x, we can set up an equation by using the fact that the sum of all the angles in an octagon is equal to (8 - 2) * 180 degrees.
Therefore, the sum of the interior angles of the octagon is:
(4x + 12)° * 8 = (8 - 2) * 180°
Simplifying the equation gives:
32x + 96 = 6 * 180
Next, we can solve for x by isolating it on one side of the equation:
32x = 6 * 180 - 96
32x = 1080 - 96
32x = 984
Finally, divide both sides of the equation by 32 to solve for x:
x = 984 / 32
x = 30.75
Therefore, the value of x is 30.75.
To find the value of x, we need to set up an equation based on the given information.
In a regular octagon, all angles are congruent. So, the measure of each angle is equal.
According to the given information, the measure of a single angle in the regular octagon is (4x + 12)°.
Since all angles are equal, we can set up the equation as follows:
(4x + 12)° = (measure of each angle)
Now, since an octagon has 8 sides, there are 8 angles in total. The sum of all the angles in an octagon is equal to (8 - 2) * 180°, which is 1080°.
So, the equation becomes:
8 * (4x + 12) = 1080
Let's solve the equation to find the value of x.
First, distribute 8 on the left side:
32x + 96 = 1080
Next, subtract 96 from both sides of the equation:
32x = 1080 - 96
32x = 984
Finally, divide both sides of the equation by 32:
x = 984 / 32
x = 30.75
Therefore, the value of x is 30.75.
The sum of the internal angles of a polygon of N sides is
(180)*(N-2) degrees.
For N = 8 (any octagon), the total is 6*180 = 1080 degrees, and in a regular octagon, each angle is 1/8 of that or 135 degrees.
Set 4x + 12 equal to 135 and solve for x. The answer will not be an integer